Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x+5y &= -2 \\ -4x+6y &= -8\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-4x = -6y-8$ Divide both sides by $-4$ to isolate $x$ $x = {\dfrac{3}{2}y + 2}$ Substitute this expression for $x$ in the first equation. $-4({\dfrac{3}{2}y + 2}) + 5y = -2$ $-6y - 8 + 5y = -2$ Simplify by combining terms, then solve for $y$ $-1y - 8 = -2$ $-1y = 6$ $y = -6$ Substitute $-6$ for $y$ in the top equation. $-4x+5( -6) = -2$ $-4x-30 = -2$ $-4x = 28$ $x = -7$ The solution is $\enspace x = -7, \enspace y = -6$.